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        Transformer家族之Weighted Transformer
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          <p><img src="https://cdn.jsdelivr.net/gh/rogerspy/blog-imgs/5396ee05ly1g5pqn3ch6zj20u092znph.jpg" alt></p>
<p>之前我们介绍了擎天柱的工作原理以及内部构造。对擎天柱已经有了深入的了解，那么本文就来介绍一下汽车人家族中的其他成员——Transformer的各种变种。</p>
<a id="more"></a>
<h1 id="1-Weighted-Transformer"><a href="#1-Weighted-Transformer" class="headerlink" title="1. Weighted Transformer"></a>1. Weighted Transformer</h1><!--more-->
<h1 id="1-Weighted-Transformer-1"><a href="#1-Weighted-Transformer-1" class="headerlink" title="1. Weighted Transformer"></a>1. Weighted Transformer</h1><p>为了更快的训练和更好的发挥<em>Transformer</em>的信息表示能力，<a href="https://arxiv.org/pdf/1711.02132.pdf" target="_blank" rel="noopener">Ahmed et al. 2017</a>提出了这种新的结构。</p>
<h2 id="1-1-模型结构"><a href="#1-1-模型结构" class="headerlink" title="1.1 模型结构"></a>1.1 模型结构</h2><p><img src="https://cdn.jsdelivr.net/gh/rogerspy/blog-imgs/5ff2618d07150a95ff4f3dc544418284e574c2.png" alt></p>
<p>模型在整体结构上和<em>Transformer</em>差不多，不同点有两个：</p>
<ul>
<li>使用<em>Multi-branch</em>代替<em>Multi-Head</em>；</li>
<li>在<em>FFN</em>上不是直接线性转换，而是<em>Multi-branch</em>线性转换后加权求和。</li>
</ul>
<p>公式如下：</p>
<script type="math/tex; mode=display">
head_i = Attention(QW_i^Q, KW_I^K, VW_I^V)</script><script type="math/tex; mode=display">
\overline{head_i} = head_i W^{O_i} \times \kappa_i</script><script type="math/tex; mode=display">
BranchedAttention(Q, K, V) = \sum_{i=1}^M \alpha_i \mathrm{FFN}_i(\overline{head_i})</script><h2 id="1-2-Multi-branch-Attention"><a href="#1-2-Multi-branch-Attention" class="headerlink" title="1.2 Multi-branch Attention"></a>1.2 Multi-branch Attention</h2><p>在<em>Weighted Transformer</em>中对<em>Attention</em>的计算和标准的<em>Transformer</em>计算过程是一致的，所以这里不做介绍。接下来对计算完的<em>scaled dot-product attention</em>的处理上，模型就在原始<em>Transformer</em>上做了修改。作为对比，我们把原始的<em>Transformer</em>在这一步的处理也列出来：</p>
<script type="math/tex; mode=display">
\overline{head_i} = head_iW^{Q_i}</script><p><em>Transformer</em>是直接将<em>heads</em>进行线性变换，而<em>Weighted transformer</em>在对每个<em>head</em>进行线性变换后还乘上一个$\kappa$参数，这个参数是可训练的，而且必须满足条件：$\sum_i \kappa_i =1$。这个参数作者称之为<em>concatenation weight</em>。</p>
<p>我们知道<em>Multi-head</em>中的每一个<em>head</em>的作用是学习句子的不同信息，<em>Transformer</em>认为每个<em>head</em>学到的信息对任务来说是平权的，因此直接将多个<em>head</em>直接等权拼接，然后线性变换。而<em>Weighted transformer</em>认为每个<em>head</em>对任务的作用是不同的，因此为每个<em>head</em>分配一个权重，用于表明这个<em>head</em>对任务的重要性，而权重的大小令模型自动从任务中学习。这种假设显然应该比<em>Transformer</em>的平权假设要更加合理。</p>
<h2 id="1-3-Weighted-point-wise-feed-forward-network"><a href="#1-3-Weighted-point-wise-feed-forward-network" class="headerlink" title="1.3 Weighted point wise feed forward network"></a>1.3 Weighted point wise feed forward network</h2><p><del>这一部分我认为作者要么是对Transformer的理解有误，要么是论文的表述不准确，在对比Transformer和Weighted Transformer的时候有点小冲突，比如作者说Transformer对应的FFN公式是$BranchedAttention(Q, K, V)=\mathrm{FFN}(\sum_i^M \overline{head_i})$，先不纠结<em>BranchedAttention</em>的函数名问题，作者认为每个<em>head</em>是通过求和， 然后再经过FFN。但是<em>Transformer</em>原始论文写的很清楚<em>head</em>是通过<em>Concat</em>拼接在一起的，并非求和。造成作者在这里使用$\sum_i^M\overline{head_i}$，我个人猜测有两个可能的原因：</del></p>
<p><del>1. 作者使用$\sum$的意图其实是<em>Concat</em></del> </p>
<p><del>2.作者可能把Transformer结构图中Add当成了对head求和</del></p>
<p><del>无论什么原因，下面的介绍我都会替换成<em>Concat</em>。另外，作者介绍<em>Weighted transformer</em>的FFN的时候使用的也是$\sum$，但是从作者在其他的地方的表述来看，这里的求和应该指的也是<em>Concat</em>。比如作者将$\kappa$命名为<em>concatenation weight</em>，另外作者认为<em>weighted transformer</em>的参数只比<em>transformer</em>多了$\alpha$和$\kappa $，所以总的参数量应该是相同的，但是如果在<em>weighted transformer</em>中这一步使用了求和的话，假设$h=8, d_k=d_v=64$， 那么FFN的输出维度应该是（batch_size, seq_len, 64），而<em>Transformer</em>的输出维度是（batch_size, seq_len, 512），这样参数量是不同的， 除非在<em>weighted transformer</em>中作者令$d_k=d_v=512$，但是如果是这样的话，每个<em>head</em>的参数又不同了，所以无论如何<em>weighted trnasformer</em>和<em>transformer</em>的参数都是不同的。因此，我认为这里应该是<em>Concat</em>。</del></p>
<blockquote>
<p>刚开始的时候由于思考的不周全，以为是作者在论文中的表述不准确，所以自己瞎讨论半天，后来发现作者的表述没有任何问题，而是自己的问题，所以上面的内容只保留删除线，不把内容删除，用来提醒自己曾经犯过的错误。</p>
<p>这里解释一下为什么作者表述是正确的，而我的理解是错误的呢？首先说作者在描述<em>transformer</em>的时候用的公式$BranchedAttention(Q, K, V)=\mathrm{FFN}(\sum_i^M \overline{head_i})$，我之前认为原始论文中这里应该是<em>Concat</em>而不应该是$\sum$，但是我忽略了一点，就是在<em>transformer</em>原始论文中，是先进行<em>Concat</em>，这个时候输出<em>tensor.shape == (batch_size, seq_len, d_model)</em>，再进行线性变换的时候$W^{O_i}$的形状应该是<em>（d_model, d_model）</em>，所以FFN的输出是<em>(batch_size, seq_len, d_model)</em>。但是本文中是先进行的线性变换，我原先想的是线性变换的<em>tensor.shape == (batch_size, seq_len, d_v)</em>，而$W^{Q_i}.shape == (d_v, d_v)$，这样得到的输出形状是<em>(batch_size, seq_len, d_v)</em>，然后平权求和，如果是这样的话就会出现我上面的错误，缺少<em>Concat</em>和输出维数对应不上的问题。但实际上这里的$W^{Q_i}.shape == (d_v, d_{model})$，这样会输出$M$个形状为<em>(batch_size, seq_len, d_model)</em>的<em>tensor</em>（这就是$\overline{head_i}=head_iW^{O_i}$这一步做的事情），然后通过沿着head方向求和就可以得到一个形状为<em>(batch_size, seq_len, d_model)</em>的<em>tensor</em>（这就是$\mathrm{FFN}(\sum \overline{head_i})$这一步做的事情），实际上本文作者的操作和<em>transformer</em>的原始论文的操作是等效的。我的思考主要问题出现在了线性变换这一步的输出上。下面我们继续跟随作者的脚步，看下他在FFN上做了什么文章。</p>
</blockquote>
<p><em>Transformer</em>在计算<em>FFN</em>的过程如下：</p>
<script type="math/tex; mode=display">
MultiHeadAttention(Q, K, V) = \mathrm{FFN}(\sum_{i=1}^M \overline{head_i})</script><p>可以看到两者的区别仍然是对不同<em>head</em>信息的加权方式不同，<em>transformer</em>仍然认为是平权的，但是<em>weighted transformer</em>认为是各有不同的权重，和$\kappa$一样，$\alpha$是从任务中学习的，且满足$\sum_i\alpha_i=1$。作者给$\alpha$取了一个名字叫做<em>addition weight</em>。</p>
<h1 id="2-模型细节"><a href="#2-模型细节" class="headerlink" title="2. 模型细节"></a>2. 模型细节</h1><p>除了以上两点修改以外，其他方面没有做任何修改。但是在训练的时候$\alpha$和$\kappa$的学习率由下式确定：</p>
<script type="math/tex; mode=display">
lr = (d_{model}/N)^{-0.5}\cdot \min(steps^{-0.5}, steps \cdot 400^{-1.5})</script><p>也就是说将<em>warmup_steps</em>改成400。</p>
<h1 id="3-代码实现"><a href="#3-代码实现" class="headerlink" title="3. 代码实现"></a>3. 代码实现</h1><h2 id="3-1-pytorch核心代码"><a href="#3-1-pytorch核心代码" class="headerlink" title="3.1 pytorch核心代码"></a>3.1 pytorch核心代码</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">MultiBranchAttention</span><span class="params">(nn.Module)</span>:</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self, depth, d_model, d_ff, n_branches, dropout)</span>:</span></span><br><span class="line">        super(MultiBranchAttention, self).__init__()</span><br><span class="line">        self.depth = depth</span><br><span class="line">        self.d_model = d_model</span><br><span class="line">        self.d_ff = d_ff</span><br><span class="line">        self.n_branches = n_branches</span><br><span class="line">        <span class="comment"># in practice, d_model == d_k * n_branches</span></span><br><span class="line">        <span class="keyword">assert</span> d_model == d_k * n_branches</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># Q, K, V Linear</span></span><br><span class="line">        self.w_q = Linear([d_model, d_model])</span><br><span class="line">        self.w_k = Linear([d_model, d_model])</span><br><span class="line">        self.w_v = Linear([d_model, d_model])</span><br><span class="line"></span><br><span class="line">        <span class="comment"># scaled dot-product attention</span></span><br><span class="line">        self.attentions = nn.ModuleList([</span><br><span class="line">            <span class="comment"># custom define</span></span><br><span class="line">            ScaledDotProductAttention(depth, dropout) <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)</span><br><span class="line">        ])</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># additional parameters for BranchedAttention</span></span><br><span class="line">        <span class="comment"># custom define</span></span><br><span class="line">        self.w_o = nn.ModuleList([Linear(depth, d_model) <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)])</span><br><span class="line">        self.w_kp = torch.rand(n_branches)</span><br><span class="line">        self.w_kp = nn.Parameter(self.w_kp/self.w_kp.sum())</span><br><span class="line">        self.w_a = torch.rand(n_branches)</span><br><span class="line">        self.w_a = nn.Parameter(self.w_a/self.w_a.sum())</span><br><span class="line"></span><br><span class="line">        <span class="comment"># Position wise feed forward network</span></span><br><span class="line">        self.ffn = nn.ModuleList([</span><br><span class="line">            <span class="comment"># custom define</span></span><br><span class="line">            PositionwiseFeedForwardNetwork(d_model, d_ff//n_branches, dropout) </span><br><span class="line">            <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)])</span><br><span class="line">        self.dropout = nn.Dropout(dropout)</span><br><span class="line">        <span class="comment"># layer normalization</span></span><br><span class="line">        <span class="comment"># custom define</span></span><br><span class="line">        self.layer_norm = LayerNormalization(d_model)</span><br><span class="line"></span><br><span class="line">        init.xavier_normal(self.w_o)</span><br><span class="line"></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">forward</span><span class="params">(self, q, k, v, attn_mask)</span>:</span></span><br><span class="line">        <span class="comment"># q: (batch_size, len_q, d_model)</span></span><br><span class="line">        <span class="comment"># k: (batch_size, len_k, d_model)</span></span><br><span class="line">        <span class="comment"># v: (batch_size, len_v, d_model) note (len_k == len_v)</span></span><br><span class="line">        residual = q</span><br><span class="line"></span><br><span class="line">        <span class="comment"># Linear</span></span><br><span class="line">        Q = self.w_q(q)  <span class="comment"># (batch_size, len_q, d_model)</span></span><br><span class="line">        K = self.w_k(k)  <span class="comment"># (batch_size, len_q, d_model)</span></span><br><span class="line">        V = self.w_v(v)  <span class="comment"># (batch_size, len_q, d_model)</span></span><br><span class="line">        </span><br><span class="line">        <span class="comment"># split</span></span><br><span class="line">        Qs = Q.split(self.depth, dim=<span class="number">-1</span>)  <span class="comment"># (b_size, len_q, depth) x n_branches</span></span><br><span class="line">        Ks = K.split(self.depth, dim=<span class="number">-1</span>)  <span class="comment"># (b_size, len_k, depth) x n_branches</span></span><br><span class="line">        Vs = V.split(self.depth, dim=<span class="number">-1</span>)  <span class="comment"># (b_size, len_v, depth) x n_branches</span></span><br><span class="line">        </span><br><span class="line">        <span class="comment"># scaled dot product attention</span></span><br><span class="line">        <span class="comment"># scaled_attn: (batch_size, len_q, d_v) x n_branch</span></span><br><span class="line">        scaled_attn = [</span><br><span class="line">            attn(Qs[i], Ks[i], Vs[i], mask) <span class="keyword">for</span> i, attn <span class="keyword">in</span> enumerate(self.attentions)</span><br><span class="line">        ]</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># multi-branch attention</span></span><br><span class="line">        <span class="comment"># outputs: (b_size, len_q, d_model) x n_branches </span></span><br><span class="line">        outputs = [self.w_o[i](scaled_attn[i]) <span class="keyword">for</span> i <span class="keyword">in</span> range(self.n_branches)]</span><br><span class="line">        outputs = [kappa * output <span class="keyword">for</span> kappa, output <span class="keyword">in</span> zip(self.w_kp, outputs)]</span><br><span class="line">        <span class="comment"># FFN</span></span><br><span class="line">        outputs = [ffn(output) <span class="keyword">for</span> ffn, output <span class="keyword">in</span> zip(self.ffn, outputs)]</span><br><span class="line">        outputs = [alpha * output <span class="keyword">for</span> alpha, output <span class="keyword">in</span> zip(self.w_a, outputs)]</span><br><span class="line"></span><br><span class="line">        <span class="comment"># output: (b_size, len_q, d_model)</span></span><br><span class="line">        output = self.dropout(torch.stack(outputs).sum(dim=<span class="number">0</span>))</span><br><span class="line">        <span class="keyword">return</span> self.layer_norm(residual + output)</span><br></pre></td></tr></table></figure>
<h2 id="3-2-tensorflow核心代码"><a href="#3-2-tensorflow核心代码" class="headerlink" title="3.2 tensorflow核心代码"></a>3.2 tensorflow核心代码</h2><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">MultiBranchAttention</span><span class="params">(tf.keras.layers.Layer)</span>:</span></span><br><span class="line">    <span class="string">"""</span></span><br><span class="line"><span class="string">    Implement Multi-branch attention layer.</span></span><br><span class="line"><span class="string">    """</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">__init__</span><span class="params">(self, depth, d_model, d_ff, n_branches, dropout)</span>:</span></span><br><span class="line">        super(MultiBranchAttention, self).__init__()</span><br><span class="line">        </span><br><span class="line">        self.depth = depth</span><br><span class="line">        self.d_model= d_model</span><br><span class="line">        self.d_ff = d_ff</span><br><span class="line">        self.n_branches = n_branches</span><br><span class="line">        self.dropout = dropout</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># K, Q, V, linear</span></span><br><span class="line">        self.wq = tf.keras.layers.Dense(d_model)</span><br><span class="line">        self.wk = tf.keras.layers.Dense(d_model)</span><br><span class="line">        self.wv = tf.keras.layers.Dense(d_model)</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># scaled dot product attention</span></span><br><span class="line">        self.attentions = [</span><br><span class="line">            <span class="comment"># custom define</span></span><br><span class="line">            scaled_dot_product_attention(depth, dropout) <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)</span><br><span class="line">        ]</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># additional parameters for BranchedAttention</span></span><br><span class="line">        self.w_o = [tf.keras.layers.Dense(d_model) <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)]</span><br><span class="line">        self.w_kp = np.random.random((n_branches,))</span><br><span class="line">        self.w_kp = tf.Variable(self.w_kp/self.w_kp.sum(), trainable)</span><br><span class="line">        self.w_a = np.random.random((n_branches,))</span><br><span class="line">        self.w_a = tf.Variable(self.w_a/self.w_a.sum(), trainable)</span><br><span class="line"></span><br><span class="line">        <span class="comment"># Position wise feed forward network</span></span><br><span class="line">        self.ffn = [</span><br><span class="line">            <span class="comment"># custom define</span></span><br><span class="line">            PositionwiseFeedForwardNetwork(d_model, d_ff//n_branches, dropout) </span><br><span class="line">            <span class="keyword">for</span> _ <span class="keyword">in</span> range(n_branches)]</span><br><span class="line">        self.dropout = tf.keras.layers.Dropout(dropout)</span><br><span class="line">        <span class="comment"># layer normalization</span></span><br><span class="line">        self.layer_norm = tf.keras.layers.LayerNormalization(epsilon=<span class="number">1e-6</span>)</span><br><span class="line">        </span><br><span class="line">        self.dense = tf.keras.layers.Dense(d_model)</span><br><span class="line">    </span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">call</span><span class="params">(self, q, k, v, mask)</span>:</span></span><br><span class="line">        residual = q</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># First linear transition step</span></span><br><span class="line">        Q = self.wq(q)  <span class="comment"># (batch_size, seq_len, d_model)</span></span><br><span class="line">        K = self.wk(k)  <span class="comment"># (batch_size, seq_len, d_model)</span></span><br><span class="line">        V = self.wv(v)  <span class="comment"># (batch_size, seq_len, d_model</span></span><br><span class="line">        </span><br><span class="line">        <span class="comment"># Split K, Q, V into multi-branch</span></span><br><span class="line">        Qs = tf.split(Q, n_branches, axes=<span class="number">-1</span>)  <span class="comment"># (batch_size, len_q, depth) x n_branches</span></span><br><span class="line">        Ks = tf.split(K, n_branches, axes=<span class="number">-1</span>)  <span class="comment"># (batch_size, len_k, depth) x n_branches</span></span><br><span class="line">        Vs = tf.split(V, n_branches, axes=<span class="number">-1</span>)  <span class="comment"># (batch_size, len_v, depth) x n_branches</span></span><br><span class="line">        </span><br><span class="line">        <span class="comment"># Scaled Dot-Product Attention step</span></span><br><span class="line">        <span class="comment"># head_i = Atteniton(QW_Q, KW_K, VW_V)</span></span><br><span class="line">        scaled_attention = [</span><br><span class="line">            attn(Qs[i], Ks[i], Vs[i], mask) <span class="keyword">for</span> i, attn <span class="keyword">in</span> enumerate(self.attentions)</span><br><span class="line">        ]</span><br><span class="line">        <span class="comment"># scaled_attention.shape == (batch_size, len_q, depth)</span></span><br><span class="line">        </span><br><span class="line">        <span class="comment"># multi-branch attention</span></span><br><span class="line">        <span class="comment"># outputs: (b_size, len_q, d_model) x n_branches </span></span><br><span class="line">        outputs = [self.w_o[i](scaled_attention[i]) <span class="keyword">for</span> i <span class="keyword">in</span> range(self.n_branches)]</span><br><span class="line">        outputs = [kappa * output <span class="keyword">for</span> kappa, output <span class="keyword">in</span> zip(self.w_kp, outputs)]</span><br><span class="line">        <span class="comment"># FFN</span></span><br><span class="line">        outputs = [ffn(output) <span class="keyword">for</span> ffn, output <span class="keyword">in</span> zip(self.ffn, outputs)]</span><br><span class="line">        outputs = [alpha * output <span class="keyword">for</span> alpha, output <span class="keyword">in</span> zip(self.w_a, outputs)]</span><br><span class="line"></span><br><span class="line">        <span class="comment"># output: (b_size, len_q, d_model)</span></span><br><span class="line">        output = self.dropout(tf.stack(outputs).sum(dim=<span class="number">0</span>))</span><br><span class="line">        <span class="keyword">return</span> self.layer_norm(residual + output)</span><br></pre></td></tr></table></figure>
<h1 id="4-参考资料"><a href="#4-参考资料" class="headerlink" title="4. 参考资料"></a>4. 参考资料</h1><ol>
<li><a href="https://arxiv.org/pdf/1711.02132.pdf" target="_blank" rel="noopener">Weighted Transformer Network for Machine Translation</a>, Ahmed et al.,  arxiv 2017 </li>
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